A manager of connections and transitions between these scenes (these are called Segues)

A nice way to manage how different controllers talk to each other

Storyboards give you a complete look at the flow of your application that you can never get from individual nib files floating around.

A reducer of all the "clutter" that happens when you have several controllers each with it's own nib file.

I have been using Storyboards for awhile now and the ONLY downside is that you can't target iOS 4 or below. Storyboards only work on devices running iOS 5 or better. Other than that, the benefits are many and the downsides are non-existent IMO.